R&D investment responses to R&D subsidies: A …...level. This is the case we de–ne as full additionality, implying @RPP @RPG = 0 , dR dRG = 2: The government then induces –rms

Working Paper No 33/10

R&D investment responses to R&D subsidies:

A theoretical analysis and a microeconometric study

by

Tor Jakob Klette

Jarle Møen

SNF project 1304

”Seamless infrastructures, business models and cultural diversity”

THE ECONOMICS OF MEDIA AND TELECOMMUNICATIONS

This report is one of a series of papers and reports published by the Institute for Research in

Economics and Business Administration (SNF) as part of its telecommunications and media

economics program. The main focus of the research program is to analyze the dynamics of the

telecommunications and media sectors, and the connections between technology, products and

business models. The project “Seamless Infrastructures, Business Models and Cultural

Diversity” is funded by The Research Council of Norway (VERDIKT).

SAMFUNNS- OG NÆRINGSLIVSFORSKNING AS

BERGEN, AUGUST 2010

ISSN 1503 – 2140

© Dette eksemplar er fremstilt etter avtale med KOPINOR, Stenergate 1, 0050 Oslo. Ytterligere eksemplarfremstilling uten avtale og i strid med åndsverkloven er straffbart og kan medføre erstatningsansvar.

R&D investment responses to R&Dsubsidies: A theoretical analysis and a

microeconometric study�

by

Tor Jakob Klettez) and Jarle Møenzz)

August 12th 2010

Abstract: Whereas many countries subsidize R&D in private companies through tax credits,subsidies to the Norwegian high-tech industries have traditionally been given as �matchinggrants�, i.e. the subsidies are targeted, and the �rms have to contribute a 50 percent own riskcapital to the subsidized projects. Our results suggest that grants do not crowd out privately�nanced R&D, but that subsidized �rms do not increase their privately �nanced R&D either.Hence, the own risk capital seems to be taken from ordinary R&D budgets. We also investigatepossible long-run e¤ects of R&D subsidies, and show that conventional R&D investment modelspredict negative dynamic e¤ects of subsidies. Our data, however, do not support this claim.On the contrary, there seem to be positive dynamic e¤ects, i.e. temporary R&D subsidies seemto stimulate �rms to increase their R&D investments even after the grants have expired. Wepropose learning-by-doing in R&D activities as a possible explanation for this, and presenta theoretical analysis showing that such e¤ects may alter the predictions of the conventionalmodels. A structural, econometric model of R&D investments incorporating such learninge¤ects is estimated with reasonable results.

JEL classi�cation: O38, O32, L53, H25, H32Keywords: Technology policy, R&D subsidies, short run additionality, long run additionality,Norwegian IT-industry

� A previous version of this paper was circulated as Klette and Moen (1998). Tor Jakob Klettesadly passed away in August 2003. He was an irreplaceable mentor, colleague and friend. Werecevied useful comments from participants at the NBER Summer Institute in 1998, and at theTSER meetings in Urbino, 1998, and Madrid, 1997. The project is �nanced by the ResearchCouncil of Norway.z University of Oslo, Department of Economics. Deceased.zz Norwegian School of Economics and Business Administration. E-mail: [email protected].

1. Introduction

The public good nature of innovation and R&D investments has attracted economists�

attention over several decades, and has received particular emphasis in the new growth

theory. The fact that R&D activities generate products that are at least partially non-

excludable and non-rivalrous was forcefully pointed out by Arrow (1962) and is a key

ingredient in the seminal Romer (1990) model. According to economic theory, there are

many di¤erent options available to deal with market failure due to externalities such

as tax credits, subsidies, extending property rights and public production. All these

policy instruments have been actively used to promote innovation and R&D activities

by most OECD governments, but both the level and the optimal mix of instruments

remain an open question.

While there is a growing literature with empirical studies of the working of R&D tax

credits, less is known about the empirical performance of other policy instruments in the

context of R&D investments.1 Our study focuses on R&D subsidies targeted at speci�c

projects, and in particular on their impact on privately funded R&D investments.

Using a panel data set for high-tech �rms, we examine the investment in R&D for

�rms receiving direct R&D grants from di¤erent public sources.2 Our main question is

whether public R&D subsidies result in a net increase or decrease in R&D expenditure,

�that is; do government funds substitute for or complement private R&D expenditures?

Our results suggest that R&D subsidies in the industries we study have been successfully

targeted at �rms that have expanded their R&D investments, and we conclude that

there is little tendency to �crowding out�. On the other hand, there does not seem to

be any signi�cant degree of �additionality�associated with the subsidies either, even

though the government requires that �rms contribute 50% own risk capital to subsidized

projects. This own risk capital seems to be taken from ordinary R&D budgets.

We also pursue the issue of dynamic or longer-run e¤ects of R&D subsidies on

R&D investments. Our empirical investigation suggests that such e¤ects are positive,

while conventional models of R&D-investments predict negative dynamic e¤ects. We

present a theoretical analysis of this question, where we argue that learning-by-doing

e¤ects in R&D may explain our empirical results. Such learning e¤ects will generate

positive feedback loops where temporary R&D subsidies increase the pro�tability of

future R&D investments. We present estimates for a structural econometric model of

R&D investment incorporating learning e¤ects in line with the theoretical model.

Mowery�s (1995) survey of the practice of technology policy points out that most

OECD countries have grants and subsidy schemes for R&D where government funds

1The literature on the response of R&D investments to tax credits has been surveyed by Gri¢ th,Sandler and Van Reenen (1995), Hall and Van Reenen (2000) and Ientile and Mairesse (2009).

2 In 2002, the Research Council of Norway introduced an R&D tax credit scheme in addition to directR&D grants. The data used in the present study do not extend into this period. The relationshipbetween the R&D tax credit and other innovation policy instruments is analyzed in Hægeland andMøen (2007).

1

SNF Working Paper No 33/10

are aimed at complementing and stimulating private R&D investments targeted at

innovations with civilian industrial applications3. Such schemes have gained popularity

among governments in the US and Europe in recent years. One such subsidy scheme

has been investigated by Irwin and Klenow (1996), in a study where they consider the

US government�s e¤ort to promote US semiconductor producers in the late 1980s and

the 1990s through subsidies to the R&D consortium called Sematech. They found that

Sematech induced members to cut their overall R&D spending which they interpreted

to be the result of the �rms eliminating excessive duplication of research. Earlier

and broader studies of US. �rms by Scott (1984) and Lichtenberg (1984, 1987), and

of German �rms by Keck (1993), have reached di¤erent conclusions. Scott (1984)

concluded that federally funded R&D in private �rms tends to stimulate the �rms�

own R&D expenditure, while Lichtenberg (1984) found no such tendency when he

controlled for problems with selection bias embedded in Scott�s estimate of the e¤ect of

federally funded R&D. Keck (1993) also argued that recipients of public R&D grants

did not increase their overall R&D activities, suggesting that public funds substituted

for private �nancing in the German �rms he studied4. It is not too surprising that

the e¤ects di¤er across these various studies, since the public R&D schemes di¤er

considerably in their aims. E.g. most of the federal funds studied by Scott (1984)

and Lichtenberg (1984, 1987) are military contracts, while the Sematech program was

aimed at industrial development based on co-operative research. See David, Hall and

Toole (2000), Ja¤e (2002) and García-Quevedo (2004) for surveys of this literature.

2. An analytical treatment of �matching grants�R&D subsidies

A common feature of Norwegian R&D grant programs is the requirement that com-

panies receiving subsidies must co-�nance the supported projects. Matching grants

have been the most common criteria, but sometimes the own risk has been more than

50% and sometimes less. Despite the formality about own risk capital it is obviously

possible that subsidies in reality crowd out private investments, or at least that some

of the private investments spent on subsidized projects would be invested in R&D even

without subsidies. To aid the discussion, and to prepare a model of matching grants

R&D-subsidies, let

R = RPP +RPG +RG (2.1)

where R is total R&D investments, RG is the R&D-subsidy received from the govern-

ment, RPG is the part of the subsidized R&D projects which a �rm has to �nance

itself, i.e. the own risk capital, and RPP is the R&D investments which the �rm un-

dertakes in non-subsidized projects. Let total R&D investments �nanced by the �rm

be RP = RPP +RPG: Matching grants imply that RPG = RG:

3See also OECD (1996), especially pp. 111-113.4See Vickery (1987) and Ergas (1987) for opposing views.

2


The full e¤ect of a subsidy on the �rms�R&D investments is given by

dR

dRG=

@RPP

@RG+@RPP

@RPG� @R

PG

@RG+@RPG

@RG+@RPG

@RPP� @R

PP

@RG+ 1

=

�2 +

@RPP

@RPG

�(2.2)

since by the de�nition of a matching grant regime @RPG

@RG= 1 and @RPP

@RG= 0 can be

assumed without loss of generality5.

Two properties of the regime are critical to the �rms�investment decision. First,

asymmetric information between private �rms and the governmental agencies allocating

the grants will a¤ect to what extent it is possible for �rms to �nance the own risk capital

using ordinary R&D budgets. Second, we do not know whether subsidized �rms receive

subsidies at the margin.

Figure 1 illustrates in a simplistic way the �rms�demand for R&D. The dashed

rectangle with base abc represents a subsidized R&D-project. w is the unit cost of

R&D in the market, e.g. the hourly wage of a researcher, and R� is the level of R&D

that the �rm will choose if it does not receive a subsidy. If the governmental agency

is perfectly informed about R�; it will only subsidize R&D projects to the right of this

level. This is the case we de�ne as full additionality, implying @RPP

@RPG= 0 , dR

dRG= 2:

The government then induces �rms to increase their total R&D by two dollars when

giving them a subsidy of one dollar because of the own risk capital requirement.

Consider now a situation where the governmental agency is not perfectly informed

about the �rms�R�; the optimal level of R&D investments without subsidies. The �rms

then want to move as much as possible of their subsidized projects to the left of R� in

order to increase the private returns to the projects.6 If the �rms succeed in moving the

projects entirely to the left of R�, there is full crowding out and @RPP

@RPG= �2, dR

dRG= 0.

Subsidies are then pure transfers, and the government does not achieves anything at

all. If, on the other hand, there is some, but not full, crowding out, @RPP

@RPG2 h�2;�1i ,

dRdRG

2 h0; 1i. One dollar spent on R&D subsidies will increase total R&D investments,but by less than a dollar since the �rms reduce their privately �nanced R&D after

receiving the subsidies. If there is neither crowding out, nor additionality, @RPP

@RPG=

�1, dRdRG

= 1: In this case a governmental R&D subsidy does not in�uence the �rms�

privately �nanced R&D, and the subsidies will therefore increase total R&D investments

dollar by dollar. With some, but not full, additionality, @RPP

@RPG2 h�1; 0i , dR

dRG2 h1; 2i :

5As RPGt = RGt ; considering@RPPt@RGt

= 0 simply means that the total e¤ect of the subsidies is measured

by the term @RPPt@RPGt

:6 In the following we disregard the possibility that the governmental agency responds to its uncertain

information about R� by being �conservative�in its grant allocation policy, so that �rms may want tomove their subsidized projects rightwards in Figure 1 in order to increase the probability of having theprojects accepted. For the purpose of this analysis, such a situation can be considered equivalent tothe case with perfect information, as there will be full additionality. The two cases will, however, notbe equivalent with respect to the commercial value of the R&D undertaken.

3


One dollar spent on R&D subsidies then increases the �rms�privately �nanced R&D,

but not with as much as a dollar. Total R&D investments will therefore increase by

less than two dollars.

In order to discuss whether the �rms are free to decide the size of the subsidized

projects, i.e. whether they are subsidized at the margin, we need to distinguish between

the unit cost of R&D in the market, and the �rms�marginal cost of R&D. Let therefore

w0 denote the �rms�marginal cost. If there is full additionality, and �rms are allowed

to decide the size of the subsidized projects, their marginal cost is w0 = 12w, and they

will expand their R&D investments until R = R�� in Figure 1. If there is less than full

additionality and the �rms are allowed to decide the size of the subsidized projects,

their marginal cost of R&D is

w0 = w

�dRP

dR

�= w

dRP

dRG

1 + dRP

dRG

!= w

�

1 + �(2.3)

where we have renamed dRP

dRG= �; and � 2 [0; 1] : With full additionality � = 1. Note

that as � ! 0; the marginal cost of R&D according to the formula above approaches

zero. The intuition behind this is that �rms can expand their R&D activities at a very

low cost if they are allowed to decide the size of subsidized projects where most of the

own risk part is privately pro�table, i.e. to the left of R�: However, the governmental

agency is bound to become suspicious if �rms apply for subsidized projects which are

large relative to their total R&D activities. This indicates that it is unlikely that

�rms are subsidized at the margin unless there is a signi�cant degree of additionality

associated with the subsidies. If the �rms are constrained with respect to the size of

the subsidized projects, their marginal cost of R&D is w0 = w.

3. The e¤ect of high-tech R&D subsidies on R&D investments: A �rstlook

3.1. Questionnaire studies

To what extent subsidies actually stimulate R&D has been an important issue when

technology programs have been evaluated. Table 2 summarizes questionnaire studies

undertaken on this account. Looking at the pooled results at the rightmost column,

about 18 percent of the supported projects would have been undertaken in full with-

out subsidies, while the subsidy was not completely crowded out in 82 percent of the

projects. Furthermore, according to the evaluation reports, 34 percent of the projects

had full additionality. Hence, these questionnaire studies suggest that R&D subsidies

as implemented by the public agencies in Norway exert a positive in�uence on the R&D

investments in private �rms. It also seems that the degree of crowding out has been

decreasing over time. This trend could indicate a learning process in the public agen-

cies implementing the subsidy schemes, but it could as well indicate that �rms have

4


become less honest when they respond to the questionnaires. One would in any case

suspect that these verbal reports are biased towards not admitting crowding out, as

this would reduce the likelihood of similar programs being launched in the future. A

more analytic approach is therefore desirable.

3.2. The e¤ect of changes in the level of subsidies on deviation from plannedR&D

One way to shed light on the e¤ect of subsidies, is to examine the correlation between

changes in the level of subsidies and the deviation from planned R&D. Such an analysis

is possible because the �rms in the R&D surveys have been asked about their R&D

investment plans both one and two years after the year of the survey. From 1982 until

1989 the investment plans were given in terms of man-years while from 1989 until 1995

they were given in nominal terms. Unfortunately, the R&D surveys were conducted

annually only in the �rst four years of the time period examined, and the correlation

between the change in R&D subsidy and the deviation between planned and performed

R&D within a one-year horizon can therefore not be calculated after 1985. From the

�rst row in Table 3 we see that the one-year horizon correlation coe¢ cient based on

the available years is essentially zero. This lack of correlation most likely indicates that

�rms know the level of subsidies they will receive one year in advance and hence that

they have already included the response to the expected subsidies in their investment

plans7

The two-year horizon results are given in Table 3, rows two and three, based on

R&D measures in man-years and nominal terms respectively. The coe¢ cients strongly

indicate that the correlation between an increase or decrease in subsidies and a devia-

tion from planned R&D, is positive and signi�cant. Our interpretation of this is that

an increase in subsidies induces the companies to undertake more research than they

otherwise would have done8. Note, however, that this does not give us any information

about the strength of the e¤ect. All that can be concluded is that there is not complete

crowding out. To determine whether there is some degree of crowding out, some or

full additionality, or maybe even more than full additionality, we need to frame the

question within a regression analysis.

7The �rms apply about a year in advance, and the data for year t are collected early in year t+ 1;i.e. year t+1 has started when the �rms give their expectations for that year. Many of the applicationsfor grants have probably been answered at that time.

8An alternative interpretation is that those who came across a good research project after they gavethe survey information both changed their plans and received subsidies. We do, however, believe thatthe time span involved is somewhat too short for this to be a plausible explanation. Within less thantwo years the �rms would have to come up with the idea, �le a detailed application for R&D support,have the application accepted and start the R&D project.

5


3.3. Crowding out or additionality: Regression analyses

In this section we regress the �rms� R&D investments on received R&D subsidies,

controlling for other factors determining R&D investments. We draw on Swenson (1992)

who summarizes the theoretical R&D investment literature into three main hypotheses

about what a¤ects the level of R&D investments in private �rms. First, expected sales

might be important if the development costs of new products or processes are �xed.

Second, technological opportunity may vary across industries and time. This will in

turn a¤ect the returns to R&D and hence the incentive to invest. Third, the degree

of appropriability is important. If it is di¢ cult to protect innovations from leaking

out to competitors, less pro�t may be made, and the incentive to innovate is reduced

accordingly.

In empirical studies, expected sales are often proxied by current sales. We have also

included the square of sales to account for possible non-linearities in size. Technological

opportunity and degree of appropriability can to some extent be handled by including

industry and time dummies. Industry dummies are, however, not su¢ cient to account

for the large heterogeneity in R&D investments found in microdata. Furthermore, as

argued by Lichtenberg (1984), unobservable �rm characteristics which positively a¤ect

the level of R&D investments are likely to be positively correlated with R&D subsidies.

To exclude this bias we have included �rm-speci�c �xed e¤ects in our regressions. Also,

since R&D subsidies are partly motivated by the belief that R&D investments might

be discriminated against in the capital markets, we have included the �rms�cash �ow

as a proxy for liquidity constraints in�uencing the level of investments9. According to

this, the regression equation is

Rit = �0 + �1Sit + �2S2it + �3CFit + �4R

Git + �t + �i + eit (3.1)

where i is a �rm index, t is a time index, Sit is sales, CFit, is cash �ow before R&D

investments, �t is a vector of time dummies, �i is a vector of �rm dummies to account

for �xed e¤ects and eit is an error term. The coe¢ cient on subsidies, �4 =@Rit@RGit

; is the

parameter of primary interest.

Our sample covers 697 observations of business units at the three digit line of busi-

ness level in the high-tech industry de�ned as ISIC 382, 383 and 385 (the manufacture

of machinery, electrical equipment and technical instruments). These have been suc-

cessfully merged with the manufacturing statistics. There are at least two observations

of every business unit, and all business units have at least 20 employees on average

over time. The variables have been de�ated, and all observations are weighted by the

square root of inverse sales to correct for heteroscedasticity.

The theory does not say anything about functional form, and various speci�cations

have been tried in the literature. A matching grants subsidy regime implies a linear

9We recognize that this cash �ow variable could also be a proxy for investment opportunities.

6


relationship between R&D investments and subsidies, whereas other studies, e.g. Bound

et al. (1984), suggest a loglinear relationship between R&D investments and sales.

We prefer a linear relationship since the e¤ect of subsidies is what we are primarily

interested in.

The results are given in Table 4, 5, 6 and 7. Column (1) reports a linear functional

form, estimated with �xed e¤ects. We consider this to be our main regression. To

test the robustness of this speci�cation, column (2) reports a linear functional form

estimated with the variables transformed to �rst di¤erences between years t and t� 2and column (3) reports a loglog functional form estimated with �xed e¤ects. The

general impression from the tables is that the three di¤erent speci�cations agree on the

main e¤ects. We will base our discussion on the results in column (1) unless otherwise

is stated.

3.3.1. Main results

From Table 4 we see that �4 is 1.03 and highly signi�cant. This suggests that there is

no crowding out, but nor does there seem to be any degree of additionality either10.

The results of the questionnaire studies indicated that the e¤ect of subsidies may have

changed over time. In a set of regressions not reported, we have investigated this by

including a dummy for observations from the 1990s in interaction with the subsidy

variable. The results do not indicate that the e¤ect of R&D subsidies has changed. We

have also run regressions where the sample is extended to include all manufacturing

industries11, but the coe¢ cient is still stable, �4 then being 0.98.

With respect to the other variables, we see that sales squared has a signi�cantly

positive coe¢ cient, implying that both small and large �rms are more R&D intensive

than medium size �rms. This �nding is supported by the empirical study of Bound et

al. (1984), but runs contrary to previous work on the relationship between size and

R&D cited in their article12. Finally, cash �ow has a positive and signi�cant e¤ect on

10Since we have controlled for �rm-speci�c e¤ects there must be a longitudinal positive correlationbetween subsidies and private investments. Firm-speci�c e¤ects, however, do not completely excludereverse causality as an explanation for our results. As pointed out by Kauko (1996), applicationsfor �nancial support are dependent on the �rms� intention to invest in R&D. If most applicationsare accepted, R&D subsidies then contain information not only on the cost of R&D but also on theintention to carry out new R&D projects. Hence, it is possible that there is a positive bias left even inthe �xed e¤ects estimates. Kauko argues that this kind of endogeneity can be controlled for by usingdata on applications �led. This, however, is only true to the extent that the �rms� own evaluationof the R&D-projects is not a¤ected by the outcome of the application. This may not be so, and inany case, data on applications �led are presently not available. We will, therefore, have to leave thisproblem unresolved. Note, however, that in addition to the possible positive bias that Kauko pointsat, there is also a possible negative bias due to measurement errors.11This sample has 2141 observations, and is constructed in the same manner as the sample based on

high-tech industries alone. The results are not reported.12 In the sample comprising all manufacturing industries, we �nd a signi�cantly negative coe¢ cient

on sales squared, indicating that this relationship may vary across industries. Note however, that thereis an obvious selection problem associated with the sample. Førre (1997) doing a thorough analysis ofthe size-R&D relationship in Norwegian manufacturing, concludes that the empirical relationship foundwhen correcting for selection bias by conventional methods, is quite sensitive to model speci�cation

7


R&D investments, suggesting that liquidity constraints may be relevant to the R&D

investment decision.

3.3.2. Di¤erences between small and large �rms

In Table 5 we report regressions studying whether there are di¤erences between small

and large �rms. We do this by including a dummy variable for small and large business

units in interaction with the subsidy and cash �ow variables. We have de�ned small

business units as units with average employment below the 25th percent percentile, i.e.

below 58 workers. Large units are de�ned accordingly as those larger than the 75th

percent percentile, i.e. having an average employment above 263 workers, cf. Table 1.

In an interview study of Norwegian manufacturing �rms, Hervik and Waagø (1997)

�nd support for the hypothesis that large �rms, having a portfolio of projects, will seek

to obtain public support for those projects they have already decided to undertake,

whereas small �rms, being less diversi�ed and possibly more liquidity constrained,

will �nd subsidies with a matching grant claim to be a stimulus making increased

R&D investments possible. It is di¢ cult to �nd support for this hypothesis in our

data. The only business units having some degree of additionality, approximately 25

percent, associated with R&D subsidies, are the large ones. For small units there

is neither crowding out, nor additionality, whereas for medium size units the point

estimate indicates about 50 percent crowding out. This �nding might be rationalized

if we extend the hypothesis of Hervik and Waagø by taking account of monitoring

costs. It is probably di¢ cult for the governmental agencies to assess whether R&D

projects for which small and medium size �rms apply, will be undertaken without

support. The hypothesis of Hervik and Waagø then explains why we �nd crowding

out for medium size �rms, but not for small �rms. Large �rms, however, are likely

to be monitored more closely by the government, as they receive large grants and are

well known �regular customers�. If these �rms apply for projects which are obviously

pro�table without subsidies, the governmental agencies might see through it, and they

can even lose credibility with respect to future applications. This may explain why we

do not �nd crowding out for these �rms.

When it comes to cash �ow, we see a similar pattern as both small and large business

units have a larger coe¢ cient than medium size units. These results are somewhat

surprising, however, and cast doubt on the cash �ow variable being able to account for

liquidity constraints. Two problems may be of relevance. First, a number of small and

medium size business units are subsidiaries of larger �rms, and the cash �ow of such

units does not contain information about the �nancial constraints they face. Second,

cash �ow may be considered a proxy for present success of the �rm and thereby for

expected future success. Expected future success increases the incentive to invest in

and outlying observations. There is a large international literature on the size-R&D relationship, cf.Cohen and Klepper (1996), but a more detailed investigation of the question is beyond the scope ofthis paper.

8


R&D. It is, however, not clear why �success�should stimulate R&D investments more

strongly in large than in small �rms.

3.3.3. Di¤erences between the e¤ect of subsidies from various public sources

The R&D surveys have detailed information on R&D investments by source of �nance,

and this makes it possible to investigate whether the e¤ect of R&D subsidies varies

across di¤erent public sources. The main governmental agencies awarding R&D sub-

sidies have traditionally been research councils, industry funds and ministries. Pure

subsidies have mostly been awarded through research councils. Grants from industry

funds are often subsidized loans, but still with an own risk capital claim. Grants from

ministries consist of various R&D contracts, many of which are defense related. We

believe that the demand for own risk capital tends to be weaker in these projects.

Table 6 reports the results of regressions with subsidies from the three main sources

included as separate variables. We see that there are no clear cut di¤erences between the

e¤ects of the various subsidies, but all regressions agree that subsidies from industry

funds have a coe¢ cient which is somewhat lower than the others. If the sample is

extended to include all manufacturing industries, the regression results suggest that

subsidies from research councils have a somewhat more positive e¤ect than subsidies

from the other two sources.13

3.3.4. Dynamic e¤ects

So far we have implicitly assumed that there are no dynamic e¤ects associated with

receiving R&D subsidies. As we will explain below, di¤erent models of accumulation of

knowledge have di¤erent predictions with respect to the dynamic e¤ects of R&D subsi-

dies. A very simple �rst approach is to include lagged R&D subsidies in the regressions

above. The results are reported in Table 7. We see that R&D subsidies lagged two

years have a signi�cantly positive e¤ect in the �xed e¤ects regression based on a linear

functional form. In column (2), using �rst di¤erences, there is also a positive coe¢ -

cient, but it is not statistically signi�cant, while in column (3), the loglog speci�cation,

there is a non-signi�cant negative coe¢ cient. When extending the sample to include

all manufacturing industries, the coe¢ cients in columns (1) and (2) increase both in

magnitude and signi�cance.14 The coe¢ cient in column (3), the loglog speci�cation,

becomes essentially zero in the larger sample.15 This suggests that R&D subsidies are

likely to have a positive dynamic e¤ect, and we would like to point out explicitly the

lack of evidence for a negative e¤ect.16

13Not reported.14The coe¢ cient in column (1) is then 0.58 and signi�cant at the 1 percent level.15Testing for di¤erences between large and small �rms, we �nd that the positive dynamic e¤ect is

strongest for small �rms. This positive small �rm e¤ect can also be detected with a loglog speci�cation.16Further evidence for the existence of this e¤ect is given in Figure 2, explained in section 4.1.

9


Dynamic e¤ects of subsidies are obviously important for public policies, as they

may in�uence the social return to subsidies. Positive dynamic e¤ects indicate that the

government permanently changes the �rms�pro�t opportunities in favor of more R&D

intensive products by awarding temporary subsidies which induce the �rms to increase

their R&D investment. A positive dynamic e¤ect, then, will increase the social return

to R&D subsidies if the level of commercial R&D is below its social optimum at the

outset.

4. Dynamic e¤ects of R&D subsidies: A theoretical analysis

In the rest of this paper we explore the dynamic e¤ects of R&D subsidies more thor-

oughly. We start out by discussing the predictions of conventional models of R&D

investments. Next we present an alternative structural model which we �nd better

suited to explain the data. This alternative model captures the idea that �rms which

have invested heavily in R&D in the past, and hence have a large knowledge capital,

will produce new knowledge more e¢ ciently than less experienced �rms. In the last

part of the paper we attempt to estimate this structural model, before summing up our

main �ndings.

4.1. The conventional R&D investment model

The most widely used speci�cation for the accumulation of knowledge capital, K, is to

treat R&D the same way as physical capital i.e.

Kt = Kt�1 (1� �) +Rt: (4.1)

where � is the rate of depreciation, cf. Griliches (1979, 1995). As is well known, with

this speci�cation, knowledge capital is adjusted so that

�0(Kt) = w0t (r + �)��wt+1 (4.2)

where �0(Kt) is the nominal marginal pro�t of knowledge capital, w0t is the marginal

cost of R&D, r is the discount rate and �wt+1 is the change in the market price of

R&D.17 From equations (4.2) and (4.1) we can deduce some simple comparative statics

results. First, by totally di¤erentiating (4.2) and adopting the standard assumption of

a decreasing marginal product of knowledge capital, we have

dRtdw0t

=r + �

�00< 0 (4.3)

17The exact expression also includes the term ��wt+1 which will be close to zero.

10


Furthermore, along an optimal investment path we have that

dRt+1dw0t

=dRt+1dKt

� dKtdRt

� dRtdw0t

= � (1� �) � 1 � r + ��00

> 0: (4.4)

Here dRt+1dKt

is calculated by totally di¤erentiating equation (4.1) and setting dKt+1equal to zero.

If �rms are subsidized at the margin, the e¤ect on optimal R&D investments of a 50

percent subsidy can be quite dramatic, at least if the pro�t function is not too concave

in K. In particular, consider the case where an R&D subsidy in the form of a matching

grant disappears. A 50 percent increase in marginal R&D costs when the subsidy

disappears, should induce a signi�cant reduction in the optimal amount of knowledge

capital. Hence, it would be optimal to deinvest or at least not to continue investing

in knowledge capital when the R&D subsidy disappears for reasonable speci�cations of

the pro�t function and the depreciation rate. In the Cobb-Douglas case, the reduction

in the optimal capital stock is 50 percent for a given level of output, if the R&D price

increases by 50 percent.

If �rms are not able to decide the size of their subsidized project, i.e. if they are not

subsidized at the margin, Rt must be considered an exogenous variable unless the R&D

subsidies are completely crowded out. Given the results in section 3, this does not seem

to be the case. Keeping the assumption of a decreasing marginal product of knowledge

capital, and a constant market price of R&D, and then totally di¤erentiating equation

(4.2) in period t + 1; when writing Kt+1 as a function of Kt�1; Rt; and Rt+1 with Rtas a function of w0t; we �nd that

dRt+1dRt

= � (1� �) < 0 (4.5)

Hence, whether or not �rms are subsidized at the margin, R&D investments in period

t+ 1 will be reduced relative to period t in �rms which lose their subsidies. This runs

contrary to the results reported in Table 7 where the e¤ect of lagged R&D, dRt+1dRt; was

positive or at least not negative.

Further support for our claim that the predictions of the conventional model do

not �t the data can be found in Figure 2, graphing the distribution of growth rates

in R&D investments from year t � 2 to year t + 2 for business units which were notsubsidized in those years, but which received subsidies in the middle year, t.18 This

is the leftmost box-and-whisker plot and may be compared with the rightmost plot of

�rms not subsidized at all.19 First note that there are no �rms which stop investing in

18Growth is measured in percent of the average level of investments in year t� 2 and year t+ 2.19The �box� in the Box-and-Whisker plots extends from the 25th percentile (x25) to the 75th per-

11


R&D when their R&D grant expires, and a large number of �rms increase their R&D

investments relative to the pre-subsidy level. Average growth for the subsidized �rms

is 11 percent, whereas average growth for the non-subsidized �rms in the rightmost

distribution is -10%. From the �gure we also see that median growth is higher for �rms

which have received subsidies.20

We conclude from the empirical results that the standard, perpetual inventory

model for knowledge accumulation, equation (4.1), is too simple to serve as a basis

for a realistic model of R&D investment behavior. Let us now consider various modi�-

cations of this model, before we turn to a more drastic respeci�cation.

4.2. Modi�cations of the conventional model: Rescue attempts

An obvious �rst step in making the perpetual inventory model more realistic is to add

a non-negativity constraint to R&D investments such that R � 0, i.e. one can not

deinvest by selling already acquired knowledge. The pattern of optimal investments in

this extended version of the model has been examined in some detail by Arrow (1968)

and others. Arrow�s analysis shows that the basic e¤ect of this extension for the case

with an expected rise in R&D costs, e.g. due to the elimination of R&D subsidies,

would be that the non-negativity constraint will tend to be binding somewhat earlier,

while the option of R&D subsidies still is in place. The intuition is that the �rms

stop their R&D investment before the subsidy is removed in order to avoid the non-

negativity constraint being too costly. Clearly, this result does not make the behavior

predicted by the model more realistic, the e¤ect is rather to the contrary, given that

�rms typically continue their R&D activity also after the R&D subsidy disappears, as

shown above.

A more promising suggestion would be to add convex adjustment costs similar to

the model used to derive Euler equations for physical capital investment as in Summers

(1981). This would make large changes in investment more costly and induce the �rms

to adjust their level of R&D more slowly. Given a reasonable speci�cation of the pro�t

function, the �rms would like to reduce their R&D investments after the R&D subsidies

have been eliminated, and they will do it gradually. However, while we �nd it natural

to think about adjustment costs for expanding the R&D activity rapidly, it is less clear

to us whether there are similar adjustment costs involved when downscaling an R&D

project making it optimal to do it gradually.

Finally, let us make a remark about another, less structural, model of R&D invest-

centile (x75), i.e. the interquartile range (IQ). The lines emerging from the box are the �whiskers�,and extends to the upper and lower adjacent values. The upper adjacent value is de�ned as the largestdata point less than or equal to x75 + (1:5 � IQ). The lower adjacent value is de�ned symmetrically.Observed data points more extreme than the adjacent values are individually plotted.20Unfortunately, the number of business units that have a pattern of subsidies which allows them to

be included in Figure 2 is very small, 13 in the leftmost distribution and 69 in the rightmost distribution.The results are, however, robust towards extending the sample to include all manufacturing industries.Doing this, the distributions consist of 29 and 234 business units respectivly.

12


ments, the so-called error-correction model widely used in time-series econometrics.

This model also has the equilibrium condition (4.2) as its point of departure, but sug-

gests that the �rms adjust to deviations from this condition with a lag and then only

gradually due to some unspeci�ed adjustment costs. Our scepticism about what such

adjustment costs are really meant to represent does not need to be repeated; the issue

here is that a lagged response of, say, two years does not make much sense for the kind

of shocks we are considering. That a �rm needs two years to realize or at least to react

to an anticipated increase in R&D costs after the grant period has expired, does not

seem very convincing.

To sum up, R&D investment models based on variations of the standard model

for knowledge accumulation predict that �rms will reduce their own R&D investments

after an R&D grant has expired or somewhat earlier, possibly down to zero if a non-

negativity constraint on R&D is binding. Otherwise, they will rely on adjustment costs

that we do not �nd convincing. These models do not seem appropriate as models of

R&D investment behavior, and we now turn to an alternative speci�cation that will

induce the somewhat sluggish adjustments we observe in the data and which o¤ers a

speci�c explanation by emphasizing learning and feedback in R&D investments and

knowledge accumulation.

4.3. Modelling R&D investments with learning-by-doing

The following accumulation equation for knowledge has been suggested by Hall and

Hayashi (1989), Jones (1995), Lach and Rob (1996) and Klette (1996) among others:

Kt+1 = K��t R�t (4.6)

� is the scale elasticity in knowledge production and � is a parameter capturing the

productiveness of R&D in generating new knowledge21. Note that the multiplicative

relationship between Kt and Rt on the right hand side of (4.6) implies positive compli-

mentarity between new R&D investments and already acquired knowledge. This can

be thought of as representing learning-by-doing in R&D.

A �rm operating from period t = 0 to t = T; and which wants to maximize its

present value, faces the following problem

maxR0;:::;RT

PV = f�(K0)� w0R0 +t=TXt=1

�t[�(Kt)� wtRt]g (4.7)

subject to (4.6). �(Kt) is the pro�t function, � is the discount factor, and wt is the

21The exact formulation is from Klette (1996). We recognize that (4.6) has the rather extreme andunrealistic implication that a �rm which stops its R&D in a single year will lose all its knowledgecapital. Alternative speci�cations that avoid this problem tend to give more complicated estimatingequations that we do not explore in this study. However, as most �rms have continous R&D activity,we believe equation (4.6) can be thought of as a reasonable approximation.

13


�rm�s average unit cost of R&D. In order to simplify the model and derive comparative

static results, we make the following assumptions:

� T = 2

� � = 1 (i.e. constant returns to scale in knowledge production.)

It is trivial to see that R2 = 0 must be part of an optimal R&D investments path as

the e¤ect of R2 does not materialize within the time period considered22. Given this,

the problem reduces to

maxR0;R1

PV =�[� (K0)� w0R0] + � [� (K1)� w1R1] + �2� (K2)

: (4.8)

The �rst order conditions are

@PV

@R0= �w00 + ��0 (K1)

�K0R0

�1��+�2� (1� �)�0 (K2)K(1��)2

0 R�(1��)�10 R�1 = 0 (4.9)

and@PV

@R1= ��w01 + �2��0 (K2)

�K1R1

�1��= 0 (4.10)

This gives the following expressions for optimal R&D investments

R1 = K1��0 R�0

��0 (K2)

w01

� 11��

(4.11)

and

R0 = K0

��

w00

� 11��"�0 (K1) + � (1� �)

��0 (K2)

� 11��

��

w01

� �1��# 11��

(4.12)

We are particularly interested in the e¤ects of varying w0; the marginal cost of R&D.

The relevant derivatives are

@R1@w01

< 0@R0@w00

< 0 (4.13)

@R1@w00

Q 0 @R0@w01

Q 0: (4.14)

The algebraic expressions are given in appendix B.

Consider now the e¤ect on R&D of a subsidy which makes investments in R&D

cheaper at the margin. The same period e¤ect is given in (4.13), and, not surprisingly,

we see that �rms will increase their R&D activity when R&D is subsidized. In this

22For simplicity we have assumed that the �rm�s knowledge capital cannot be sold in the market.

14


respect, the model performs similarly to the traditional framework, cf. equation (4.3).

The dynamic e¤ects, however, are more interesting. From the leftward derivative in

(4.14) we see that a temporary subsidy at t = 0, may induce the �rm to undertake

more R&D also in the next period even if it is not subsidized then. This contrasts

the conventional model of R&D investments, where the dynamic e¤ect is negative, cf.

equation (4.4). Note also that it is the diminishing returns to knowledge capital which

make (4.14) indeterminate. If we isolate the learning-by-doing feature of our model

by assuming that �0 (K) is constant23 and thereby that �00 (K) = 0; we see from the

expressions in appendix B that the pure e¤ect of learning is positive, i.e. @R1@w00

< 0: The

existence of learning-by-doing in R&D is therefore able to explain the empirical results

in Table 7. From (4.14) we also see that a known subsidy at t = 1; may induce the �rm

to increase its R&D activity already at t = 0: This is another result which is impossible

within the conventional framework built on the analogy between physical capital and

R&D. A �rm which knows that capital will be subsidized at t = 1; and not at t = 0;

will de�nitely not increase its investments in the period when capital is not subsidized.

The intuition behind the dynamic behavior of our model is that when there is

learning-by-doing in R&D, increased R&D today will make �rms more e¢ cient R&D

performers in future periods through their increased knowledge capital. This increases

the pro�tability of future R&D. Likewise, if a �rm gets to know that the price of R&D

will be lowered in the future, it will �nd it pro�table to increase its present R&D, as

this will make it a more e¢ cient R&D performer in future periods when it will increase

its R&D activity due to the lower price.

Note that a subsidy regime which induces �rms to increase their same-period R&D

without altering the marginal price will have the same dynamic e¤ects as

@R1@R0

R 0 @R0@R1

R 0 (4.15)

The rightmost result is derived by treating R1 as an exogenous variable and using

implicit derivation on (4.9). Once again, going to appendix B and setting �00 (K) = 0;

we �nd a certain positive dynamic e¤ect.

5. A structural, econometric analysis of the dynamic e¤ects of R&Dsubsidies

We now want to pursue a more complete structural modelling of R&D investments suit-

able for empirical applications, building on the framework of Klette (1996) and Klette

and Johansen (1998). First we present the model and extends it by incorporating

uncertainty in the knowledge production function, as uncertainty is an important char-

acteristic of R&D investments. Next we modify the model to handle R&D subsidies,

and derive the estimation equation.

23 In this case the optimal level of investment is not de�ned within the conventional framework.

15


5.1. An empirical in�nite horizon model with uncertainty in knowledge pro-duction

To incorporate uncertainty in the knowledge production function, rewrite (4.6)

Kt+1 = K��t R�t "t (5.1)

where "t is a mean-one stochastic factor accounting for the randomness in research

activities. One way to identify the optimal investment behavior given the accumulation

equation above is to consider the Bellman-equation

V (Kt) = maxRt

f�t (Kt)� wtRt + �Et [V (Kt+1)]g

= maxRt

f�t (Kt)� wtRt + �Et [�t+1 (Kt+1)� wt+1Rt+1]

+�2Et [V (Kt+2 )]g; (5.2)

where Kt+1 is as speci�ed in (5.1). Et is the expectation operator, conditioned on the

�rm�s information set available when it makes its decision about the investment Rt:

We can identify an optimal path by considering the marginal change in Rt+1 induced

by a marginal change in Rt such that an optimal path remains unchanged from period

t+ 2 onwards, i.e.

EtdKt+2 = Etdh(K��

t R�t "t)��R�t+1"t+1

i

= Et

�� (�� ) Kt+2

RtdRt + �

Kt+2Rt+1

dRt+1

�= Et

��Kt+2

�(�� ) dRt

Rt+dRt+1Rt+1

��= 0 (5.3)

implying that, in expectational terms,

dRt+1dRt

= � (�� ) Rt+1Rt

: (5.4)

The �rst order condition associated with (5.2), given that Kt+2 is �xed is

wt = � Et

��0t+1(Kt+1)

@Kt+1@Rt

� wt+1dRt+1dRt

�(5.5)

which, using (5.1) and (5.4), can be restated as

wtRt = � Et [��0t+1(Kt+1)Kt+1] + �(�� )Et [wt+1Rt+1]: (5.6)

A common speci�cation of the pro�t function implies that �0t(Kt)Kt = St, where

16


St is sales (see Klette, 1996). Hence, an optimal R&D investment path requires that

wtRt = �� Et [St+1] + �(�� )Et [wt+1Rt+1] (5.7)

The Euler equation (5.7) gives a tight relationship between R&D expenditures in period

t and expected sales and planned R&D expenditures in period t+ 1.

5.2. Incorporating �matching grants�R&D subsidies in the empirical model

To incorporate public R&D-subsidies letRt = RPPt +RPGt +RGt . Based on the discussion

in section 2, we have three analytically interesting situations which imply di¤erent

modi�cations to the Euler equation:

1. If there is full crowding out, we cannot distinguish between the R&D investments

of subsidized and non-subsidized �rms, and the Euler equation does not change.

In this situation it is also obvious that the �rms cannot be subsidized at the

margin.

2. If there is less than full crowding out, but not a signi�cant degree of additionality,

�rms are not likely to be subsidized at the margin. The subsidies do, however,

increase the �rms�total R&D-investments. A situation where there is signi�cant

additionality, but where �rms nonetheless are constrained with respect to the

size of the subsidized project, will have the same implications with respect to the

Euler equation. We will discuss these below.

3. If there is signi�cant additionality, and the �rms are unconstrained with respect to

the size of the subsidized project, the marginal cost of R&D is given by equation

(2.3), with � = 1 as a limiting case implying that there is full additionality.

In the cases grouped under item 2 above, w0 is not a¤ected by the subsidy, hence

w0 = w: Furthermore, RG and RPG are exogenous to our analysis. In these cases,

introducing public R&D-subsidies induces two changes in the Bellmann equation (5.2),

and these are the replacement of R by RPP as the control variable and the replacement

of R by�RPP +RPG

�inside the brace. The �rst order condition (5.5), then becomes24

wt = � Et

"�0t+1(Kt+1)

@Kt+1

@RPPt� wt+1

dRPPt+1dRPPt

#(5.8)

which can be rewritten

wtRt = � �Et [�0t+1(Kt+1)Kt+1] + �(�� )Et [wt+1Rt+1]: (5.9)

24We assume here thatdRPGt+1dRPPt

= 0: In a more complete model where one endogenizes the allocation

of R&D subsidies, one would want to allow the amount of privately �nanced R&D invested this year toin�uence the amount of subsidies received next year. Such a �ne point, however, is beyond the scopeof this exposition.

17


Note that this equation, maybe somewhat surprisingly, is identical to equation (5.6). As

long as a �rm is not subsidized at the margin, therefore, its optimal R&D investment

path will follow (5.6), and hence (5.7), whether it receives subsidies or not. This,

however, is not to say that receiving subsidies is without implications for the �rms�

investment decision, something which can be seen by rewriting (5.7) specifying the

various components of Rt and Rt+1:

wt�RPPt +RPGt +RGt

�= �� Et [St+1]

+�(�� )Et [wt+1�RPPt+1 +R

PGt+1 +R

Gt+1

�] (5.10)

We see that a �rm which does not receive subsidies at time t (when it decides RPPt ),

but which does expect to receive subsidies at time t+ 1, will undertake more R&D at

time t than a �rm with the same expectations about sales, but which does not expect

to receive subsidies in the next period. There is a simple rationale for this: the �rm

knows that it will receive some additional R&D resources in the next period which,

by assumption, cannot be completely crowded out. According to equation (5.1), these

resources can be utilized more e¢ ciently the higher its knowledge capital base, Kt+1;

at that time. Given this, it is optimal for the �rm to �prepare�for the expected R&D-

expansion in advance by building up more knowledge through an increase in RPPt : Due

to the same dynamic e¤ect, a �rm which receives subsidies at time t; but which does

not expect to receive subsidies at time t+1, will do more R&D at time t+1; than a �rm

with the same expectations about sales, but which does not receive subsidies at time

t: This is because the subsidized �rm starts out at time t+ 1 with a larger knowledge

capital base then the non-subsidized �rm, something which makes it a more e¢ cient

�knowledge producer�. For this reason the subsidized �rm �nds it optimal to invest

more in R&D at time t+1 than it would have done without the subsidy at time t: This

will of course also increase its knowledge capital at time t+ 2; relative to the scenario

without a subsidy at time t; and consequently we can conclude that a temporary R&D

subsidy which is not completely crowded out, will have a lasting positive impact on the

�rm�s future R&D investments. This e¤ect will of course be more signi�cant the less

crowding out or more additionality there is associated with the subsidy.

Let us now consider the case described under item 3 above, i.e. the case with

additionality and where the �rms decide the size of the subsidized projects. In a period

where �rms are subsidized, their marginal cost of R&D is given by equation (2.3). We

must then distinguish between three di¤erent situations;

� (i) the �rms are subsidized at the margin at time t, but do not expect to besubsidized at the margin at time t+ 1:

� (ii) the �rms are not subsidized at the margin at time t, but expect to be subsi-dized at the margin at time t+ 1:

18


� (iii) the �rms are subsidized at the margin at time t, and expect to be subsidizedat the margin at time t+ 1:

When the �rms are not subsidized at the margin, their marginal cost of R&D is

w0 = w; and this makes it possible to easily incorporate a fourth category within the

framework that we are now building up. This category comprises all other �rms, i.e.

� (iv) those �rms which are not subsidized at the margin at time t, and which donot expect to be subsidized at the margin at time t+ 1.

Using dummy variables to distinguish between �rms in di¤erent situations, the

Euler equation (5.7), becomes�D2 +D4 + (D1 +D3)

�

1 + �

�wtRt = �� Et [St+1]

+�(�� )Et��D1 +D4 + (D2 +D3)

�

1 + �

�wt+1Rt+1

�(5.11)

where D1 is one for �rms in category (i) and zero otherwise, D2 is one for �rms in

category (ii) and zero otherwise, D3 is one for �rms in category (iii) and zero other-

wise, and D4 is one for �rms in category (iv) and zero otherwise. Given the application

and data collection procedure, cf. footnote 7, it seems likely that the �rms are well

informed one year in advance about whether or not they will receive subsidies. Assum-

ing, therefore, perfect foresight with respect to next year�s subsidies, equation (5.11)

can be reformulated

wtRt = �� Et [St+1] +��

�f(D1 +D3) � Et [St+1]g

+�(�� )Et [wt+1Rt+1]

+�(�� )

�fD1 � Et [wt+1Rt+1]g

��(�� )1 + �

fD2 � Et [wt+1Rt+1]g : (5.12)

Note that as � ! 0; some of the coe¢ cients go to in�nity, once again re�ecting the

fact that �rms are not likely to be subsidized at the margin for such values of �;

and, thus, that there are not likely to be �rms in category (i)-(iii) if � is low. Note

also that if some �rms are misclassi�ed as belonging to one of the categories (i)-(iii)

when belonging to category (iv), these observations still have all the relevant variables

included. They do, however, also have non-zero additional variables, namely those

involving dummies in (5.12). From an econometric point of view, this can be interpreted

as the inclusion of irrelevant variables, and the estimated coe¢ cients for these variables

should be insigni�cant and close to zero if in fact the majority of �rms are not subsidized

at the margin.

19


5.3. Estimating the Euler Equation

We start out by assuming that subsidized �rms are subsidized at the margin. This

hypothesis can be tested. Equation (5.12) can be estimated and will, given the necessary

data, identify the degree of additionality through the parameter � if the hypothesis is

correct. If it is wrong, it will be falsi�ed through non-signi�cant parameters for the

terms involving dummy variables.

The Norwegian R&D surveys contain information on planned R&D, Et [wt+1Rt+1],

but not on expected sales. To circumvent this problem, we have used real sales in the

following year as a proxy, and instrumented this variable by its present and lagged value

in order to avoid the endogeneity problem thus involved. The sales data are merged in

from the manufacturing statistics.

Another problem is to decide which �rms belong to which of the four categories

determining the values of the dummy variables. Assuming perfect foresight one year

ahead is reasonable and helps, but we have annual R&D data only for the period 1982-

1985. For the period 1985-1995, the R&D surveys were only conducted every second

year, and, hence, for these years we do not know which �rms received a subsidy in period

t + 1: One way to proceed, is to assume that �rms received subsidies at time t + 1 if

they received subsidies both at time t and t + 2; as there is positive autocorrelation

in subsidy allocation. Likewise, therefore, it seems reasonable to assume that �rms

did not receive subsidies at time t + 1 if they did not receive subsidies at time t nor

at time t+ 2 : Similar reasoning cannot be adopted for �rms which received subsidies

at t, but not at time t + 2, or the other way around. These observations, therefore,

have to be excluded. Unfortunately, then, there are rather few observations in our

data set which can identify the coe¢ cients in front of the last two terms in equation

(5.12), as the majority of the observations are from the period 1985-1995, and it is

only a small fraction of the �rms that change their subsidy recipient status in the years

1982-1985 . There are 17 observations in category (i), 13 observations in category (ii),

31 observations in category (iii) and 121 observations in category (iv). To correct for

heteroscedasticity, all observations are weighted by the square root of inverse sales.

Further information about the variable construction can be found in appendix A.

The estimation results are given in Table 8. The coe¢ cients of equation (5.12) are

reported in column (1). Two of the dummy variable terms are statistically insigni�cant

and have opposite signs to those predicted by theory. The last one is correctly signed

and weakly signi�cant. Using the correctly signed and weakly signi�cant coe¢ cient to

identify � gives b� = 7:45; a value way outside the theoretical range, � 2 h0; 1i. Thismeans that this coe¢ cient is also too close to zero to have a meaningful interpretation.

We conclude from this that the hypothesis underlying the regression is wrong, i.e. that

�rms are not subsidized at the margin. This view is also supported by our result of no

additionality in section 3.3, cf. the discussion at the very end of section 2.

If the subsidized �rms are not subsidized at the margin, all �rms will have to be

20


reclassi�ed to category (iv), and the dummy variable terms will not be part of the

regression equation. Table 8, column (2) reports the estimation results based on this

assumption. With this speci�cation, both coe¢ cients are signi�cant at conventional

levels.

6. Conclusions and future research

Whereas many countries subsidize R&D in private companies through tax credits, subsi-

dies to the Norwegian high-tech industries have mainly been given as �matching grants�,

i.e. the subsidies are targeted, and the �rms have to contribute a 50 percent own risk

capital to the projects. It is, however, an open question to what extent this induces

�rms to increase their total R&D investments as they may reduce non-subsidized R&D

activities upon receiving an R&D grant. Our results suggest that grants do not crowd

out privately �nanced R&D, but that subsidized �rms do not increase their privately �-

nanced R&D either. Hence, the own risk capital seems to be taken from ordinary R&D

budgets, and there is no �additionality�associated with matching grants subsidies.

Our results also suggest that the subsidies most e¢ ciently stimulate R&D invest-

ments in small and large �rms as opposed to medium size �rms. One hypothesis which

may explain this is that R&D investments in small �rms are liquidity constrained,

whereas large �rms are so closely monitored by the governmental agencies awarding

the subsidies that it is di¢ cult for them to receive support for projects which are prof-

itable without subsidies. A variable measuring the �rms�cash �ow does not indicate

that small �rms are liquidity constrained, however. This might be because this variable

rather measures the present success of the �rms, something which may be considered

a proxy for future success and thereby for the incentive to invest in R&D. Our main

result of neither crowding out, nor additionality, seems to be robust both over time and

across a wider sample of manufacturing �rms than those belonging to the traditional

high-tech industries. In addition, there are no clear cut di¤erences between the e¤ects

of subsidies awarded by research councils, industry funds and ministries.

We have also investigated possible long-run e¤ects of R&D subsidies, and we have

shown that the conventional perpetual inventory model of R&D investments predicts

the dynamic e¤ects of subsidies to be negative. There is, however, no empirical evidence

supporting this claim. On the contrary, there seems to be a positive dynamic e¤ect, i.e.

temporary R&D subsidies seem to stimulate �rms to increase their R&D investments

even when the grants have expired. We have argued that learning-by-doing in R&D

activities is a possible explanation for this, and our theoretical analysis shows that

such e¤ects alter the predictions of the conventional models. The intuition behind the

dynamic behavior of our model is that with learning-by-doing in R&D, increased R&D

in one period makes �rms more e¢ cient R&D performers in future periods through

increased knowledge capital. This increases the pro�tability of future R&D.

A structural, econometric model of R&D investments incorporating such learning

21


e¤ects has been estimated with reasonable results. These results suggest that matching

grants subsidies do not a¤ect the �rms�marginal price of R&D, a �nding which is to

be expected if there is little or no additionality associated with subsidies in the period

in which they are awarded.

In future research, it is our ambition to combine the Euler equation in this paper

with the performance equation of Klette (1996), in order to identify the parameters

necessary to predict the strength of the dynamic e¤ects, and not least to estimate the

returns to private and public R&D investments.

22


Appendix A: Data

The core of the high-tech industries is the manufacture of o¢ ce machinery and com-

munication equipment, i.e. ISIC 3825 and 3832. This is the kind of production most

intensely promoted by the government, but subsidies have been awarded to a wider set

of high-tech projects than those performed within these two sub-industries. To obtain

a sample of reasonable size, and to avoid classi�cation problems associated with com-

panies having production and research activities covering a broader class of products

than ISIC 3825 and 3832, we have used production and R&D aggregated to the three-

digit line of business level. For the purpose of empirical analysis in this paper, we have

therefore de�ned high-tech as the manufacture of machinery, electrical equipment and

technical instruments, i.e. ISIC 382, 383 and 385. These industries have many R&D

performing �rms and are technologically related.

Data sources

The analysis uses merged data from R&D surveys and time series �les of the man-

ufacturing statistics. The manufacturing statistics of Statistics Norway is an annual

census of all plants in the Norwegian manufacturing industries. From this source we

use information on sales and cash �ow. See Halvorsen et al. (1991) for documentation

of the data base. R&D surveys are available for the years 1982-85, 1987, 1989, 1991,

1993 and 1995. These surveys were carried out by the Royal Norwegian Council for

Scienti�c and Industrial Research (NTNF) until 1989 and by Statistics Norway from

1991. See Skorge et al. (1996) for de�nitions and industry level �gures. We have aggre-

gated R&D expenditures to the three digit (ISIC) line of business level before merging

these variables to the manufacturing statistics. This means that our observations are

not �rms, but business units. A business unit is de�ned as all production activities

within a �rm having the same three digit ISIC classi�cation. Single plant �rms consist

of one business unit, whereas multiplant �rms may consist of several business units.

Approximately 75 percent of all manufacturing �rms are single plant �rms.

Sample construction

The R&D surveys have close to full coverage of �rms with more than 20 employees in

the industries studied, i.e. ISIC 382, 383 and 385. There are altogether 1658 time-year

observations of business units at the three-digit line of business level in these industries

included in the surveys. 1278 of these are successfully merged to the manufacturing

statistics. 714 observations had a time average of more than 20 employees, positive R&D

investments and were included in at least two surveys. This sample was moderately

trimmed leaving 697 observations for our empirical investigations. Outliers were de�ned

as �rms having value added per man-hour below the one percent percentile, above the

99 percent percentile or having an R&D intensity above the 99 percent percentile. Table

23


1 gives some sample statistics.

Variable construction

Sales are measured as the value of gross production corrected for taxes and subsidies.

Cash Flow before R&D is measured as sales subtracted labor expenses, material ex-

penses and rentals. To this measure are added R&D expenses �nanced by own means

as given in the R&D surveys. Nominal variables in the manufacturing statistics are

de�ated using industry level de�ators from the Norwegian national accounts. The R&D

variables include both intramural and extramural R&D expenditures. The R&D ex-

penditures, consisting mainly of labor costs, are de�ated using an index based on the

movement of average wage in ISIC 382, 383 and 385.

For the years 1982-1987, planned R&D is reported in man-years. When estimating

the Euler equation, this variable is converted to Norwegian kroner using the �rm-speci�c

ratio between R&D man-years and R&D investments in the year of the survey, and in-

�ated with the growth in the R&D price index during the following year. Another

weakness with the data for planned R&D is that they in 1995 include R&D-related

capital investments. To adjust for this, the variable is reduced by the 1995 share of

R&D-related capital investments in the sum of R&D and R&D-related capital invest-

ments.

There are also problems related to the instruments used in the Euler equation. We

do not have data for sales in 1996, and the 1995-observations therefore lack our proxy

for expected sales. To circumvent this, we have constructed the proxy using sales in

1995, if possible, multiplied by the �rm-speci�c growth rate from 1994 to 1995. We

use a similar procedure for �rms that exit the panel before 1995, and to construct the

instrumental variable, lagged sales, where this is missing.

24


Appendix B: Algebraic expressions for the derivatives in section 4.3

@R1@w01

= f�00 (K2)�K1R1

�1��w01

�"K11� � (��)

11��

��0 (K2)

w01

� �1��#�1

g�1 < 0 (6.1)

@R0@w00

= � K0w00 (1� �)

��

w00

� 11��

�"�0 (K1) + � (1� �)

��0 (K2)

� 11��

��

w01

� �1��#

�f1� K01� �

��

w00

� 11��

�"�0 (K1) + � (1� �)

��0 (K2)

� 11��

��

w01

� �1��# 11��

�"�00 (K1)

@K1@R0

+ �

��

w01

� �1��

�00 (K2)@K2@R0

#g�1 < 0 (6.2)

@R1@w00

= �

�K0R0

�1�� 0 (K2)w01

� 11�� @R0

@w00

+K1�

0 (K2)

(1� �)

��

w01

�2�00 (K2)

@K2@R0

@R0@w00

Q 0 (6.3)

@R0@w01

=�K01� �

��0 (K2)

w00

� 11��

�"��

w01

(�0 (K1) + � (1� �)

��0 (K2)

� 11��

��

w01

� �1��)# �

1��

��00 (K2)

@K2@R1

@R1@w01

� �

w01

�R 0 (6.4)

@R1@R0

=

(�

��0 (K2)

w01

� 11��

+��

w1 (1� �)R0

��0 (K2)

w01

� �1��

�00 (K2)@K2@R0

)

��K0R0

�1��R 0 (6.5)

25


@R0@R1

= �� (1� �)K(1��)20 R1��

2

0

��00 (K2)

@K2@R1

+ �R�1�0 (K2)

��f� (1� �)K(1��)2

0 R1��2

0

��00 (K2)

@K2@R0

��1 + �2 � �

� R�1R0�0 (K2)

�+�00 (K1)K

1��0 R0 � (1� �)�0Kg�1 R 0 (6.6)

26


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29


i

Figure 2: The change in R&D accompanying a Subsidy Regime change

Perc

ent gro

wth

in R

&D

fro

m t-2

to t+

2

Box-and-Whisker plots for firms not receiving sub. at t-2 and t+2

-200

-100

0

100

200 Firms subsidized at t Firms not subsidized at t

w w

R R*

a b c

1 w2

RPG = RG

w

Figure 1: The Firm’s Demand Curve for R&D

R**


ii

Table 1: Sample Statistics ISIC 382, 383 and 385 Total no. of observations 697 no. of business units 192 average no. of observations per business unit 3,6 Observations with subsidies 300 subsidized from research councils 197 subsidized from industry funds 111 subsidized from ministries 98 Observations of small business units (Average no. of workers<25th perc.) 176 Observations of large business units (Average no. of workers>75th perc.) 168 Average no. of workers per business unit 334 25th. Percentile 58 Median 107 75th. Percentile 263 Average R&D intensity 0,07 Median R&D intensity 0,04 Average subsidy share (excluding observations with zero subsidy) 0,23 Median subsidy share (excluding observations with zero subsidy) 0,17 Sample: R&D performing business units in 1982-1995 included in at least two R&D surveys, having at least 20 workers on average, and being successfully merged with the manucaturing statistics. The sample is moderately trimmed. See appendix A for further details. Table 2: Norwegian Interview Studies of the Crowding Out Effect of R&D Subsidies Study GF84 HB89 HBW92 HW97 OKOH97 Sample size 54 191 213 200 49 Weighted Time periode 78-82 80-84 84-89 90-95 92-95 average Project done without subsidy 34 % 33 % 15 % 6 % 2 % 18 % Project delayed or diminished 46 % 45 % 46 % 57 % 28 % 48 % Project not done without subsidy 20 % 23 % 40 % 37 % 70 % 34 % Studies: GF84; Grønhaug and Fredriksen (1984), HB89; Hervik and Brunstad (1989), HBW92; Hervik, Berge and Wicksteed (1992), HW97; Hervik and Waagø (1997), OKOH97; Olsen et.al. (1997). Respondents who could not or did not answer are not included. Only in HB89, where the full sample consisted of 230 projects, was this cathegory of any significance. Table 3: Correlation Coefficients Between Deviation From Planned R&D and Change in R&D-Subsidy

Corr.coef. Sign.level No. of obs. One year horizon: Planned R&D in man-years 0,006 0,95 107 Two year horizon: Planned R&D in man-years 0,34 0,00 147 Two year horizon: Planned R&D in kroner 0,17 0,10 99 9 observations in 1991 where deviation from planned R&D measured in man-years and kroner has opposite signs are excluded.


iii

Table 4: The Effect of R&D-Subsidies on Total R&D (1) (2) (3) Functional form linear Linear loglog Estimation method fe Diff fe Sales -0,025** (0,0088) 0,0050 (0,0080) -0,62 (1,52) Sales squared 1,5e-8*** (4,7e-7) -2,9e-10 (5,0e-9) 0,020 (0,046) Total R&D-subsidy 1,03*** (0,16) 1,06*** (0,17) 0,064*** (0,012) Cash flow 0,087*** (0,025) 0,097*** (0,033) 0,019 (0,015) R-Square 0,95 0,39 0,90 No. of observations 697 379 697 The observations are weighted by the square root of inverse sales [log of sales in (3)] to correct for heteroscedasticity. Time dummies included in all regressions. The variables have been deflated. Robust standard errors in parenthesis. * Significant at the 10% level ** Significant at the 5% level *** Significant at the 1% level Table 5: The Effect of R&D-Subsidies on Total R&D: Differences Between Small and Large Firms (1) (2) (3) Functional form Linear linear Loglog Estimation method Fe diff Fe Sales -0,022*** (0,0084) 0,0076 (0,0074) -0,55 (1,50) Sales squared 1,3e-8*** (4,8e-9) -2,6e-9 (5,7e-9) 0,018 (0,046) Total R&D-subsidy 0,51* (0,27) 0,47** (0,22) 0,056*** (0,014) *small firm dummy 0,48 (0,32) 0,63** (0,29) 0,022 (0,025) *large firm dummy 0,74** (0,36) 0,74** (0,33) 0,012 (0,032) Cash Flow 0,041* (0,025) 0,034 (0,025) 0,0093 (0,019) *small firm dummy 0,028 (0,055) 0,040 (0,059) 0,015 (0,032) *large firm dummy 0,056 (0,039) 0,077* (0,047) 0,017 (0,038) R-Square 0,95 0,41 0,90 No. of observations 697 379 697 The observations are weighted by the square root of inverse sales [log of sales in (3)] to correct for heteroscedasticity. Time dummies are included in all regressions. The variables have been deflated. Robust standard errors in parenthesis. Large and small firms are defined as firms with average employment below the 25th percetile and above the 75th percentile respectively.


iv

Table 6: The Effect of R&D-Subsidies on Total R&D: Differences Between Sources of Subsidies (1) (2) (3) Functional form Linear linear Loglog Estimation method Fe diff Fe Sales -0,024*** (0,0087) 0,0050 (0,0080) -0,58 (1,57) Sales squared 1,4e-8*** (4,8e-9) -4,8e-10 (5,0e-9) 0,020 (0,048) Subsidy from research councils 0,95*** (0,23) 1,57*** (0,59) 0,043*** (0,012) Subsidy from industry funds 0,72*** (0,29) 0,97*** (0,26) 0,029*** (0,011) R&D grants from ministries 1,17*** (0,25) 1,07*** (0,24) 0,053*** (0,016) Cash flow 0,085*** (0,024) 0,098*** (0,033) 0,020 (0,015) R-Square 0,95 0,39 0,89 No. of observations 697 379 697 *** Significant at the 1% level ** Significant at the 5% level * Significant at the 10% level The observations are weighted by the square root of inverse sales [log of sales in (3)] to correct for heteroscedasticity. Time dummies are included in all regressions. The variables have been deflated. Robust standard errors in parenthesis. Table 7: The Effect of R&D-Subsidies on Total R&D: Dynamics (1) (2) (3) Functional form linear linear loglog Estimation method fe Diff fe Sales -0,020** (0,019) -0,0058 (0,013) 3,38 (3,35) Sales squared 1,2e-8*** (1,1e-8) 4,4e-9 (9,0e-9) -0,099 (0,10) Total R&D-subsidy 1,15*** (0,24) 0,96*** (0,32) 0,051*** (0,020) Total R&D-subsidy at t-2 0,36* (0,20) 0,16 (0,15) -0,019 (0,016) Cash flow 0,083** (0,037) 0,087** (0,035) 0,038 (0,024) R-Square 0,96 0,29 0,91 No. of observations 379 181 379 The observations are weighted by the square root of inverse sales [log of sales in (3)] to correct for heteroscedasticity. Time dummies are included in all regressions. The variables have been deflated. Robust standard errors in parenthesis. * Significant at the 10% level ** Significant at the 5% level *** Significant at the 1% level


v

Table 8: Euler Equation Estimates (1) (2) Expected sales 0,0023* (0,0013) 0,0033** (0,0016) * dummy for subsidy only at time t or both at t and t+1 (D1+D3) -0,0020 (0,0029) Planned R&D 0,82*** (0,017) 0,090*** (0,031) * dummy for subsidy only at time t (D1) -0,22 (0,17) * dummy for subsidy only at time t+1 (D2) -0,097* (0,051) Root MSE 5,7 13,6 No. of observations 182 528 The observations are weighted by the square root of inverse sales to correct for heteroscedasticity. Robust standard errors in parenthesis. 2SLS regression on nominal values. Sales at period t+1 is used as proxy for expected sales and instrumented with sales in period t and t-1. * Significant at the 10% level ** Significant at the 5% level *** Significant at the 1% level



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Martine Ryland Hvordan påvirker termineringsavgifter små mobiloperatører

som One Call?


Terje Ambjørnsen Customer Ignorance, price cap regulation and rent-seeking in

Øystein Foros mobile roaming

Ole-Chr. B. Wasenden SNF Working Paper No 05/09

Hans Jarle Kind Market shares in two-sided media industries

Frank Stähler SNF Working Paper No 04/09

Hans Jarle Kind Should utility-reducing media advertising be taxed?

Marko Koethenbuerger SNF Working Paper No 03/09

Guttorm Schjelderup

Morten Danielsen Muligheter og utfordringer i fremtidens rubrikkmarked

Magnus Frøysok på Internett


Johanne R. Lerbrekk Markedssvikt i TV-markedet og behovet for offentlige kanaler

- sett i lys av digitaliseringen av bakkenettet


Per E. Pedersen The effects of variety and bundling on choice and satisfaction:

Herbjørn Nysveen Applications to new telecommunication and media services


Øystein Foros The interplay between competition and co-operation: Market

Bjørn Hansen players’ incentives to create seamless networks



Per E. Pedersen An exploratory study of business model design and customer

Leif B. Methlie value in heterogeneous network services

Herbjørn Nysveeen SNF Report No 09/08, Bergen

Hans Jarle Kind Business models for media firms: Does competition matter for

Tore Nilssen how they raise revenue?

Lars Sørgard SNF Working Paper No 21/08, Bergen

Helge Godø Structural conditions for business model design in new

Anders Henten information and communication services – A case study of

multi-play and MVolP in Denmark and Norway

SNF Working Paper No 16/08, Bergen

Hans Jarle Kind On revenue and welfare dominance of ad valorem taxes in two-

Marko Koethenbuerger sided markets

Guttorm Schjelderup SNF Working Paper No 08/08, Bergen

Øystein Foros Price-dependent profit-shifting as a channel coordination

Kåre P. Hagen device

Hans Jarle Kind SNF Working Paper No 05/08, Bergen

Hans Jarle Kind Efficiency enhancing taxation in two-sided markets

Marko Koethenbuerger SNF Working Paper No 01/08, Bergen

Guttorm Schjelderup

Documents

R&D investment responses to R&D subsidies: A …...level. This is the case we de–ne as full additionality, implying @RPP @RPG = 0 , dR dRG = 2: The government then induces –rms